Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 11

Speedup: 1.0×

• 34.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \left(t - x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Python

def code(x, y, z, t):
	return x + ((y - z) * (t - x))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - z) * Float64(t - x)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - z) * (t - x));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - z\right) \cdot \left(t - x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (* (- y z) (- t x))))

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((y - z) * (t - x))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - x));
}

Python

def code(x, y, z, t):
	return x + ((y - z) * (t - x))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(y - z) * Float64(t - x)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((y - z) * (t - x));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(t - x\right) \cdot \left(y - z\right) + x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ (* (- t x) (- y z)) x))

C

double code(double x, double y, double z, double t) {
	return ((t - x) * (y - z)) + x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((t - x) * (y - z)) + x
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((t - x) * (y - z)) + x;
}

Python

def code(x, y, z, t):
	return ((t - x) * (y - z)) + x

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(t - x) * Float64(y - z)) + x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((t - x) * (y - z)) + x;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(t - x), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \left(t - x\right) \cdot \left(y - z\right) + x \]
4. Add Preprocessing

Alternative 2: 65.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-149}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -2.3e+26)
     t_1
     (if (<= y 1.12e-149)
       (fma z x x)
       (if (<= y 2.3e-17) (* (- z) t) (if (<= y 7.6e+19) (fma z x x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.3e+26) {
		tmp = t_1;
	} else if (y <= 1.12e-149) {
		tmp = fma(z, x, x);
	} else if (y <= 2.3e-17) {
		tmp = -z * t;
	} else if (y <= 7.6e+19) {
		tmp = fma(z, x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -2.3e+26)
		tmp = t_1;
	elseif (y <= 1.12e-149)
		tmp = fma(z, x, x);
	elseif (y <= 2.3e-17)
		tmp = Float64(Float64(-z) * t);
	elseif (y <= 7.6e+19)
		tmp = fma(z, x, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.3e+26], t$95$1, If[LessEqual[y, 1.12e-149], N[(z * x + x), $MachinePrecision], If[LessEqual[y, 2.3e-17], N[((-z) * t), $MachinePrecision], If[LessEqual[y, 7.6e+19], N[(z * x + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e26 or 7.6e19 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(t - x\right) \cdot y} \]

      3. lower--.f64 81.4

         \[\leadsto \color{blue}{\left(t - x\right)} \cdot y \]

   5. Applied rewrites 81.4%

      \[\leadsto \color{blue}{\left(t - x\right) \cdot y} \]

   if -2.3000000000000001e26 < y < 1.11999999999999999e-149 or 2.30000000000000009e-17 < y < 7.6e19

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + -1 \cdot \left(z \cdot \left(t - x\right)\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(t - x\right)\right) + x} \]

      2. *-commutative N/A

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t - x\right) \cdot z\right)} + x \]

      3. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \left(t - x\right)\right) \cdot z} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(t - x\right), z, x\right)} \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(t - x\right)\right)}, z, x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)}\right), z, x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)}\right), z, x\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)}, z, x\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - t}, z, x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{x} - t, z, x\right) \]

      11. lower--.f64 89.2

          \[\leadsto \mathsf{fma}\left(\color{blue}{x - t}, z, x\right) \]

   5. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x - t, z, x\right)} \]

   6. Taylor expanded in x around inf

      \[\leadsto x \cdot \color{blue}{\left(1 + z\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.2%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{x}, x\right) \]

   if 1.11999999999999999e-149 < y < 2.30000000000000009e-17

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot t} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(y - z\right) \cdot t} \]

      3. lower--.f64 46.4

         \[\leadsto \color{blue}{\left(y - z\right)} \cdot t \]

   5. Applied rewrites 46.4%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot t} \]

   6. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot z\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 32.5%

      \[\leadsto \left(-z\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Developer Target 1: 96.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

C

double code(double x, double y, double z, double t) {
	return x + ((t * (y - z)) + (-x * (y - z)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((t * (y - z)) + (-x * (y - z)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((t * (y - z)) + (-x * (y - z)));
}

Python

def code(x, y, z, t):
	return x + ((t * (y - z)) + (-x * (y - z)))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(t * Float64(y - z)) + Float64(Float64(-x) * Float64(y - z))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((t * (y - z)) + (-x * (y - z)));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] + N[((-x) * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

  (+ x (* (- y z) (- t x))))